Course
4 Unit 7 - Functions and Symbolic Reasoning1st Edition

In Course 4, the
mathematical strands in the Contemporary Mathematics in Context
program become increasingly blended within units. The content of this
unit is from both the algebra and functions strand and the geometry and
trigonometry strand. (See the descriptions of Course
4 Units.)

Unit Overview

Functions and
Symbolic Reasoning extends student ability to manipulate symbolic
representations of exponential, common and natural logarithmic, and trigonometric
functions and to solve exponential, logarithmic, and trigonometric equations.
Trigonometric identities are developed and proved or disproved. Geometric
representations of complex numbers are used to reason about and to find
roots of complex numbers.

Unit Objectives

To use properties of exponents to transform exponential expressions
into equivalent exponential expressions

To solve exponential equations

To use relationships between logarithms and exponentials to
write logarithmic equations in forms without logarithms

To know and be able to use the definitions of the six trigonometric
functions of angles in standard position

To know and be able to use the fundamental trigonometric identities

To prove a statement of equality is an identity

To solve trigonometric equations

To represent complex numbers geometrically

To interpret multiplication of complex numbers geometrically

To use DeMoivre's Theorem to find all the roots of a complex
number

Sample Overview

There are two different
samples from Functions and Symbolic Reasoning. The first sample
consists of Investigations 1 and 2 from Lesson 2, "Reasoning with Trigonometric
Functions." These investigations introduce the cosecant, secant, and
cotangent functions and begin work with trigonometric identities.

The second sample
is the "Looking Back" lesson for this unit. This lesson is intended to
provide students with tasks that will encourage them to look back at the
unit as a whole. Students review, synthesize, and apply the knowledge
gained during the study of the unit.

Instructional
Design

Throughout the curriculum,
interesting problem contexts serve as the foundation for instruction.
As lessons unfold around these problem situations, classroom instruction
tends to follow a common pattern as elaborated under Instructional
Design.

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How the Algebra
and Functions Strand Continues

Algebraic representations
of surfaces and conic sections are introduced in Unit 8, Space
Geometry.
A unit from the algebra and functions strand that develops understanding
and skill in the use of standard spreadsheet operations while reviewing
and extending many of the basic algebra topics from Courses 1-3 is recommended
for students intending to pursue college programs in social, management,
and some of the health sciences or humanities.